Question

The Bezier curve in the following figure is defined by 4 control points. P,-(0. O), Pi = (1, 1), P2 (3, 2), Ps- (4, 0). a) b) Find the equation of the Bezier curve Find the point on the curve at u 0.5 1 0

Answer 1

equation for four points is

P(t)=(1−t)^3P0+3t(1−t)^2P1+3t^2(1-t)P2+t^3P3

we can also write this in terms of x and y find their values separately

x(t)=(1−t)^3x0+3t(1−t)^2x1+3t^2(1-t)x2+t^3x3

y(t)=(1−t)^3y0+3t(1−t)^2y1+3t^2(1-t)y2+t^3y3

if putting values for t=0.5

P(t) = (1/8)P0+3*(1/2)*(1/4)P1+3*(1/4)*(1/2)P2+(1/8)P3

P(t) = (1/8)P0+(3/8)P1+(3/8)P2+(1/8)P3

P(t) = 1/8((0,0)+3*(1,1)+3*(3,2)+(4,0))

P(t) = 1/8((0,0)+(3,3)+(9,6)+(4,0))

P(t) = 1/8((16,9))

P(0.5)=(2,9/8)

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